Eggs seem like they should be a commodity item, with one egg being about the same as another. But if you've been to a grocery store lately, you know that egg types are proliferating as fast as new breakfast cereals! You can buy eggs based on their size and color, as well as the organic content of the feed the chickens eat, the meat content of the feed the chickens eat, the amount of freedom the chickens have while eating, etc. And now farmers are starting to differentiate themselves using nutritional claims.
It turns out that the eggs you bought are patented, and the patent reveals that all of the benefits come from the diet fed to the chickens. What a chicken eats has an important effect on what ends up in the chicken's egg. By feeding the chicken a diet rich in vitamin E and low in saturated fats, the eggs end up being high in vitamin E and low in saturated fat.
There are two other ways that a farmer or breeder could change the contents of an egg. One way involves the traditional selective breeding approach. If the farmer were to analyze eggs from 100 chickens and find the ones with, for example, the lowest cholesterol in their eggs, the farmer could then breed just those chickens. By repeating this process over several generations, the farmer may be able to create a stable line of chickens that have lower amounts of cholesterol in their eggs. Farmers use this technique all the time -- they breed the sweetest corn plants in an attempt to make sweet corn sweeter, etc.
The other way would involve some form of genetic engineering, in which one or more genes are added to or subtracted from the chicken's DNA. See How Cells Work for a discussion of DNA and genetic engineering techniques.
Here is the patent for the eggs you purchased and a link: